Search results for: Lagrange multipliers

Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Boguslaw Schreyer

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In this paper, a general dynamical model is derived using the Lagrange formalism. The two masses: sprang and unsprang are included in a six-degree of freedom model for a sprung mass. The unsprung mass is included and shown only in a simplified model, although its equations have also been derived by an author. The simplified equations, more suitable for the computer model of robot’s dynamics are also shown.

Keywords: dynamics, mobile, robot, wheeled mobile robots

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Authors: Mujde Turkkan, Nurkan Yagiz

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In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modelled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: ride comfort, air spring, bus, fuzzy logic controller

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Hafiz Md. Hasan Babu, Khandaker Mohammad Mohi Uddin, Nitish Biswas, Sarreha Tasmin Rikta, Nuzmul Hossain Nahid

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Nanomedicine and bioengineering use biological systems that can perform computing operations. In a biocomputational circuit, different types of biomolecules and DNA (Deoxyribose Nucleic Acid) are used as active components. DNA computing has the capability of performing parallel processing and a large storage capacity that makes it diverse from other computing systems. In most processors, the multiplier is treated as a core hardware block, and multiplication is one of the time-consuming and lengthy tasks. In this paper, cost-effective DNA multipliers are designed using algorithms of molecular DNA operations with respect to conventional ones. The speed and storage capacity of a DNA multiplier are also much higher than a traditional silicon-based multiplier.

Keywords: biological systems, DNA multiplier, large storage, parallel processing

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Authors: Mujde Turkkan, Nurkan Yagiz

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The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: active suspension system, air suspension, bus model, sliding mode control

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Authors: F. Fekak, A. Gravouil, M. Brun, B. Depale

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During an earthquake, a bridge crane may be subjected to multiple impacts between crane wheels and rail. In order to model such phenomena, a time-history dynamic analysis with a multi-scale approach is performed. The high frequency aspect of the impacts between wheels and rails is taken into account by a Lagrange explicit event-capturing algorithm based on a velocity-impulse formulation to resolve contacts and impacts. An implicit temporal scheme is used for the rest of the structure. The numerical coupling between the implicit and the explicit schemes is achieved with a heterogeneous asynchronous time-integrator.

Keywords: bridge crane, earthquake, dynamic analysis, explicit, implicit, impact

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Authors: Avaneesh Vaishwar, Badam Singh Kushvah, Devi Prasad Mishra

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We studied the variation in orbital elements of Mars and Jupiter for a time span of 200 thousand years by using secular theory. Here we took Sun oblateness into account and considered the first two zonal gravity constants (J2 and J4) for showing the effect of Sun oblateness on the orbital elements of Mars and Jupiter. We found that in both cases (with and without Sun oblateness) the variation in orbital elements of Mars and Jupiter is periodic moreover in case of the Sun oblateness, the period of variation in orbital elements is decreasing for both the planets.

Keywords: lagrange's planetary equation, orbital elements, planetary system, secular theory

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: array signal processing, direction-of-arrival, antenna arrays, Eigenvalues, Eigenvectors, Lagrange multiplier

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Authors: Mohammed Sabri Ali Akresh

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The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM.

Keywords: harmonic equations, coordinate system, projections, algorithms, parallels

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Authors: Abbas Cheraghi

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A key predistribution scheme provides one method to distribute secret ahead of time. Blom’s scheme is a symmetric threshold key exchange protocol in cryptography. The scheme was proposed by the Swedish cryptographer Rolf Blom. In this kind of scheme, trusted authority gives each user a secret key and a public identifier, which enables any two users to create independently a shared key for communicating between each other. However, if an attacker can compromise the keys of at least Known numbers of users, he can break the scheme and reconstruct every shared key. In this paper generalized Blom’s Scheme by multivariate Lagrange interpolation formula. This scheme is a form of threshold secret sharing scheme. In this new scheme, the amount of information transmitted by the trusted authority is independent of the numbers of users. In addition, this scheme is unconditionally secure against any individual user.

Keywords: key predistribution, blom’s scheme, secret sharing, unconditional secure

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Authors: Lubna Naz, Munir Ahmad, G. M. Arif

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This study analyzes static and dynamic welfare impacts of food price changes for various landholding groups in Pakistan. The study uses three classifications of land ownership, landless, small landowners and large landowners, for analysis. The study uses Panel Survey, Pakistan Rural Household Survey (PRHS) of Pakistan Institute of Development Economics Islamabad, of rural households from two largest provinces (Sindh and Punjab) of Pakistan. The study uses all three waves (2001, 2004 and 2010) of PRHS. This research work makes three important contributions in literature. First, this study uses Quadratic Almost Ideal Demand System (QUAIDS) to estimate demand functions for eight food groups-cereals, meat, milk and milk products, vegetables, cooking oil, pulses and other food. The study estimates food demand functions with Nonlinear Seemingly Unrelated (NLSUR), and employs Lagrange Multiplier and test on the coefficient of squared expenditure term to determine inclusion of squared expenditure term. Test results support the inclusion of squared expenditure term in the food demand model for each of landholding groups (landless, small landowners and large landowners). This study tests for endogeneity and uses control function for its correction. The problem of observed zero expenditure is dealt with a two-step procedure. Second, it creates low price and high price periods, based on literature review. It uses elasticity coefficients from QUAIDS to analyze static and dynamic welfare effects (first and second order Tylor approximation of expenditure function is used) of food price changes across periods. The study estimates compensation variation (CV), money metric loss from food price changes, for landless, small and large landowners. Third, this study compares the findings on welfare implications of food price changes based on QUAIDS with the earlier research in Pakistan, which used other specification of the demand system. The findings indicate that dynamic welfare impacts of food price changes are lower as compared to static welfare impacts for all landholding groups. The static and dynamic welfare impacts of food price changes are highest for landless. The study suggests that government should extend social security nets to landless poor and categorically to vulnerable landless (without livestock) to redress the short-term impact of food price increase. In addition, the government should stabilize food prices and particularly cereal prices in the long- run.

Keywords: QUAIDS, Lagrange multiplier, NLSUR, and Tylor approximation

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Authors: Elimhan N. Mahmudov

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The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

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Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

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Erosion in pipe bends caused by particles is a major obstacle in the oil and gas fields and might cause the breakdown of production equipment. This work studied the effects imposed by flow velocity and impact of solid particles diameter in an elbow; erosion rate was verified with experimental data using the computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model was employed to calculate the air/solid particle flow in an elbow. One erosion model and three-particle rebound models were used to predict the erosion rate on the 90° elbows. The generic erosion model was used in the CFD-based erosion model, and after comparing it with experimental data, results showed agreement with the CFD-based predictions as observed.

Keywords: erosion, prediction, elbow, computational fluid dynamics

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Authors: Aymen Laadhari, Gábor Székely

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In this work, the hemodynamics in the sinuses of Valsalva after Transcatheter Aortic Valve Implantation is numerically examined. We focus on the physical results in the two-dimensional case. We use a finite element methodology based on a Lagrange multiplier technique that enables to couple the dynamics of blood flow and the leaflets’ movement. A massively parallel implementation of a monolithic and fully implicit solver allows more accuracy and significant computational savings. The elastic properties of the aortic valve are disregarded, and the numerical computations are performed under physiologically correct pressure loads. Computational results depict that blood flow may be subject to stagnation in the lower domain of the sinuses of Valsalva after Transcatheter Aortic Valve Implantation.

Keywords: hemodynamics, simulations, stagnation, valve

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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This paper investigates the nonlinear dynamic response of a mechanical torque limiter which is used to protect drive parts from overload (helical transmission gears). The system is driven by four excitations: two external excitations (aerodynamics torque and force) and two internal excitations (two mesh stiffness fluctuations). In this work, we develop a dynamic model with lumped components and 28 degrees of freedom. We use the Runge Kutta step-by-step time integration numerical algorithm to solve the equations of motion obtained by Lagrange formalism. The numerical results have allowed us to identify the sources of vibration in the wind turbine. Also, they are useful to help the designer to make the right design and correctly choose the times for maintenance.

Keywords: two-stage helical gear, lumped model, dynamic response, torque-limiter

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Authors: Shiksha Jain, Ramesh Mishra

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One of the most widely used complex signals processing operation is filtering. The most important FIR digital filter are widely used in DSP for filtering to alter the spectrum according to some given specifications. Power consumption and Area complexity in the algorithm of Finite Impulse Response (FIR) filter is mainly caused by multipliers. So we present a multiplier less technique (DA technique). In this technique, precomputed value of inner product is stored in LUT. Which are further added and shifted with number of iterations equal to the precision of input sample. But the exponential growth of LUT with the order of FIR filter, in this basic structure, makes it prohibitive for many applications. The significant area and power reduction over traditional Distributed Arithmetic (DA) structure is presented in this paper, by the use of slicing of LUT to the desired length. An architecture of 16 tap FIR filter is presented, with different length of slice of LUT. The result of FIR Filter implementation on Xilinx ISE synthesis tool (XST) vertex-4 FPGA Tool by using proposed method shows the increase of the maximum frequency, the decrease of the resources as usage saving in area with more number of slices and the reduction dynamic power.

Keywords: multiplier less technique, linear phase symmetric FIR filter, FPGA tool, look up table

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Authors: Hussein Altartouri

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In this paper the kinematic and kinetic models of an omnidirectional holonomic mobile robot is presented. The kinematic and kinetic models form the OmniDrive model. Therefore, a mathematical model for the robot equipped with three- omnidirectional wheels is derived. This model which takes into consideration the kinematics and kinetics of the robot, is developed to state space representation. Relative analysis of the velocities and displacements is used for the kinematics of the robot. Lagrange’s approach is considered in this study for deriving the equation of motion. The drive train and the mechanical assembly only of the Festo Robotino® is considered in this model. Mainly the model is developed for motion control. Furthermore, the model can be used for simulation purposes in different virtual environments not only Robotino® View. Further use of the model is in the mechatronics research fields with the aim of teaching and learning the advanced control theories.

Keywords: mobile robot, omni-direction wheel, mathematical model, holonomic mobile robot

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: M. Vimal Raj, S. Sakthivel Murugan

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Underwater images degrade their quality due to atmospheric conditions. One of the major problems in an underwater image is motion blur caused by the imaging device or the movement of the object. In order to rectify that in post-imaging, parameters of the blurred image are to be estimated. So, the point spread function is estimated by the properties, using the spectrum of the image. To improve the estimation accuracy of the parameters, Optimized Polynomial Lagrange Interpolation (OPLI) method is implemented after the angle and length measurement of motion-blurred images. Initially, the data were collected from real-time environments in Chennai and processed. The proposed OPLI method shows better accuracy than the existing classical Cepstral, Hough, and Radon transform estimation methods for underwater images.

Keywords: image restoration, motion blur, parameter estimation, radon transform, underwater

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Authors: Hyun-Ho Lee, Kee-Won Kim

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The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: Xie Kefeng, Zhang He

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For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, dynamics, Lagrange, parallel platform

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Authors: M. Iruleswari, A. Jeyapaul Murugan

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Most fundamental part used in many Digital Signal Processing (DSP) application is a Finite Impulse Response (FIR) filter because of its linear phase, stability and regular structure. Designing a high-speed and hardware efficient FIR filter is a very challenging task as the complexity increases with the filter order. In most applications the higher order filters are required but the memory usage of the filter increases exponentially with the order of the filter. Using multipliers occupy a large chip area and need high computation time. Multiplier-less memory-based techniques have gained popularity over past two decades due to their high throughput processing capability and reduced dynamic power consumption. This paper describes the design and implementation of highly efficient Look-Up Table (LUT) based circuit for the implementation of FIR filter using Distributed arithmetic algorithm. It is a multiplier less FIR filter. The LUT can be subdivided into a number of LUT to reduce the memory usage of the LUT for higher order filter. Analysis on the performance of various filter orders with different address length is done using Xilinx 14.5 synthesis tool. The proposed design provides less latency, less memory usage and high throughput.

Keywords: finite impulse response, distributed arithmetic, field programmable gate array, look-up table

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Authors: Qaiser Munir, Hamid Hussain

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Oil prices are believed to have a major impact on several economic indicators, leading to several instances where a comparison between oil prices and a trade deficit of oil-importing countries have been carried out. Building upon the narrative, this paper sheds light on the ongoing debate by inquiring upon the possibility of asymmetric linkages between oil prices, industrial production, exchange rate, whole price index, and trade deficit. The analytical tool used to further understand the complexities of a recent approach called nonlinear auto-regressive distributed lag model (NARDL) is utilised. Our results suggest that there are significant asymmetric effects among the main variables of interest. Further, our findings indicate that any variation in oil prices, industrial production, exchange rate, and whole price index on trade deficit tend to fluctuate in the long run. Moreover, the long-run picture denotes that increased oil price leads to a negative impact on the trade deficit, which, in its true essence, is a disproportionate impact. In addition to this, the Wald test simultaneously conducted concludes the absence of any significant evidence of the asymmetry in the oil prices impact on the trade balance in the short-run.

Keywords: trade deficit, oil prices, developing economy, NARDL

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Authors: Chiou-Yng Lee, Wen-Yo Lee, Chieh-Tsai Wu, Cheng-Chen Yang

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Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit-level and digit-level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba schemes, and used that to derive a novel scalable multiplier architecture. Analytical results show that the proposed multiplier provides a trade-off between space and time complexities. Our proposed multiplier is modular, regular, and suitable for very-large-scale integration (VLSI) implementations. It involves less area complexity compared to the multipliers based on traditional decomposition methods. It is therefore, more suitable for efficient hardware implementation of pairing based cryptography and elliptic curve cryptography (ECC) in constraint driven applications.

Keywords: digit-serial systolic multiplier, elliptic curve cryptography (ECC), Karatsuba algorithm (KA), shifted polynomial basis (SPB), pairing computation

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Authors: Raj Kumari Bahl, Sotirios Sabanis

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In this paper, we are concerned with the valuation of the first Catastrophic Mortality Bond that was launched in the market namely the Swiss Re Mortality Bond 2003. This bond encapsulates the behavior of a well-defined mortality index to generate payoffs for the bondholders. Pricing this bond is a challenging task. We adapt the payoff of the terminal principal of the bond in terms of the payoff of an Asian put option and present an approach to derive model-independent bounds exploiting comonotonic theory. We invoke Jensen’s inequality for the computation of lower bounds and employ Lagrange optimization technique to achieve the upper bound. The success of these bounds is based on the availability of compatible European mortality options in the market. We carry out Monte Carlo simulations to estimate the bond price and illustrate the strength of these bounds across a variety of models. The fact that our bounds are model-independent is a crucial breakthrough in the pricing of catastrophic mortality bonds.

Keywords: mortality bond, Swiss Re Bond, mortality index, comonotonicity

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

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In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: carbon nanotubes, vibration control, piezoelectric layers, elastic foundation

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Authors: Chung-Chun Hsiao, Yu-Kai, Ting, Kai-Yuan Liu, Pang-Wei Yen, Jia-Ying Tu

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In this paper, a new design of spherical robotic system based on the concepts of gimbal structure and gyro dynamics is presented. Robots equipped with multiple wheels and complex steering mechanics may increase the weight and degrade the energy transmission efficiency. In addition, the wheeled and legged robots are relatively vulnerable to lateral impact and lack of lateral mobility. Therefore, the proposed robotic design uses a spherical shell as the main body for ground locomotion, instead of using wheel devices. Three spherical shells are structured in a similar way to a gimbal device and rotate like a gyro system. The design and mechanism of the proposed robotic system is introduced. In addition, preliminary results of the dynamic model based on the principles of planar rigid body kinematics and Lagrangian equation are included. Simulation results and rig construction are presented to verify the concepts.

Keywords: gyro, gimbal, lagrange equation, spherical robots

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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